A unicorn doesn't have to be a horse. Technically, any animal with only one horn is a unicorn, which means there are actually a few unicorns in nature and even more animals that can be perceived as a unicorn. In the case of billy goats, they can even be made into unicorns:

Historical literature is very precise when describing the appearance of unicorns, noting their white color, cloven hooves and billygoat-like beard among other characteristics. Some self-styled veterinarian/alchemists have evidently noted these clues and have taken it upon themselves to create their very own unicorns from goats.

The process of making a unicorn goat is patented, but the basic concept involves translating the horn buds from a baby goat onto the center of its head.